f ( x ) = 6 x³ - 13 x² - 4 x + 15
f ( - 1 ) = 6 · ( - 1 ) - 13 · 1 - 4 · ( - 1 ) + 15 = - 6 - 13 + 4 + 15 = - 19 + 19 = 0
( 6 x³ - 13 x² - 4 x + 15 ) : ( x + 1 ) = 6 x² - 19 x + 15
-6 x³ - 6 x²
--------------------
- 19 x² - 4 x
+ 19 x² + 19 x
----------------------
15 x + 15
-15 x - 15
------------
R ( x ) = 0
After that:
6 x² - 19 x + 15 = 6 x² - 10 x - 9 x + 15 =
= 2 x( 3 x - 5 ) - 3 ( 3 x - 5 ) = ( 3 x - 5 ) ( 2 x - 3 )
Answer:
The completely factored form is: ( x + 1 ) · ( 3 x - 5 ) · ( 2 x - 3 )